A Hierarchical Approach to Monadic Second-Order Logic over Graphs

@inproceedings{Schiering1997AHA,
  title={A Hierarchical Approach to Monadic Second-Order Logic over Graphs},
  author={Ina Schiering},
  booktitle={CSL},
  year={1997}
}
The expressiveness of existential monadic second-order logic is investigated over several classes of finite graphs among them the graphs of bounded tree-width. A hierarchical approach to the decomposition of graphs is introduced which is related to the notion of tree decomposition. Among other results we show that existential monadic second-order logic on graphs of bounded tree-width is not closed under complement. 
Expressivité de la logique du premier ordre, de la logique dynamique propositionnelle sans étoile et des automates communicants. (Expressivity of first-order logic, star-free propositional dynamic logic and communicating automata)
TLDR
It is shown that, over MSCs, star-free PDL syntax can be simplified into a logic that is closer to linear temporal logic (LTL), but still equivalent to first-order logic, and this result applies, directly or indirectly, to various natural classes of structures.
Graph structurings : some algorithmic applications
Tous les problemes definissables en logique du second ordre monadique peuvent etre resolus en temps polynomial dans les classes de graphes qui ont une largeur de clique bornee. La largeur de clique
Décompositions structurelles et sémantiques Rapport préliminaire
Dans le cas des modeles graphiques, meme les plus simples comme les CSP (reseaux de contraintes), les de-compositions generalement proposees dans la litterature s'interessent pour l'essentiel a la

References

SHOWING 1-10 OF 12 REFERENCES
On Logics, Tilings, and Automata
  • W. Thomas
  • Computer Science, Mathematics
    ICALP
  • 1991
TLDR
A notion of “graph acceptor” is introduced which can specify monadic second-order properties and allows to treat known types of finite automata in a common framework.
Elements of an automata theory over partial orders
  • W. Thomas
  • Computer Science
    Partial Order Methods in Verification
  • 1996
A model of nondeterministic nite automaton over ((nite) partial orders is introduced. It captures existential monadic second-order logic in expressive power and generalizes classical word automata
Easy Problems for Tree-Decomposable Graphs
Monadic Second-Order Logic Over Rectangular Pictures and Recognizability by Tiling Systems
TLDR
It is shown that a set of pictures is recognized by a finite tiling system iff it is definable in existential monadic second-order logic, which generalizes finite-state recognizability over strings and also matches a natural logic.
NONDETERMINISM VERSUS DETERMINISM OF FINITE AUTOMATA OVER DIRECTED ACYCLIC GRAPHS
TLDR
Three types of nite-state graph automata are compared over directed acyclic graphs (where vertices and edges are labelled) and it is shown that deterministic versions are strictly weaker.
Graph minors. I. Excluding a forest
Monadic generalized spectra
...
...